A construction of codes with linearity from two linear codes

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• 作者：Chengju Li ; Sunghan Bae ; Haode Yan
• 关键词：Codes ; Weight enumerators ; Quadratic bent functions ; Simplex codes
• 刊名：Cryptography and Communications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：9
• 期：1
• 页码：55-69
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Data Structures, Cryptology and Information Theory; Coding and Information Theory; Communications Engineering, Networks; Information and Communication, Circuits; Mathematics of Computing;
• 出版者：Springer US
• ISSN：1936-2455
• 卷排序：9

文摘

Let \(\mathbb {F}_{p}\) be a finite field, where p is a prime. This paper presents a new construction of a code \(\mathcal C\) over \(\mathbb {F}_{p^{2}}\) from two linear codes over \(\mathbb {F}_{p}\), which has \(\mathbb {F}_{p}\)-linearity and its minimum distance is equal to its minimum nonzero weight. Based on our construction, we shall determine the weight enumerators of some codes defined by quadratic bent functions and simplex codes. It will be shown that these codes have a few nonzero weights.